The negative binomial distribution Quiz

1. $X\sim\mathrm{NB}(2,0.4)$. Find $\mathrm{P}(X=3)$.

• A. $0.0960$
• B. $0.1920$
• C. $0.2880$
• D. $0.0640$

2. $X\sim\mathrm{NB}(5,0.5)$. Find $\mathrm{E}(X)$.

• A. $2.5$
• B. $5$
• C. $10$
• D. $25$

3. $X\sim\mathrm{NB}(2,0.2)$. Find $\mathrm{Var}(X)$.

• A. $40$
• B. $10$
• C. $8$
• D. $4$

4. Which variable is best modelled by a negative binomial distribution?

• A. The number of heads in 20 tosses of a fair coin
• B. The number of tosses up to the first head
• C. The number of emails received in an hour
• D. The number of tosses needed to obtain 5 heads

5. $X\sim\mathrm{NB}(2,0.5)$. Find $\mathrm{P}(X\leq3)$.

• A. $0.25$
• B. $0.375$
• C. $0.5$
• D. $0.75$